Trustworthy scientific inference with generative models

TL;DR

This paper introduces FreB, a rigorous protocol that transforms AI-generated posteriors into valid confidence regions, ensuring trustworthy scientific inference even with complex, intractable likelihoods.

Contribution

The paper presents FreB, a novel method that guarantees valid confidence regions from generative models, improving reliability in scientific inference across various disciplines.

Findings

FreB produces confidence regions with correct coverage probabilities.

It effectively handles dataset shifts and model misspecifications.

FreB enhances trustworthiness of AI-based scientific conclusions.

Abstract

Generative artificial intelligence (AI) excels at producing complex data structures (text, images, videos) by learning patterns from training examples. Across scientific disciplines, researchers are now applying generative models to "inverse problems" to directly predict hidden parameters from observed data along with measures of uncertainty. While these predictive or posterior-based methods can handle intractable likelihoods and large-scale studies, they can also produce biased or overconfident conclusions even without model misspecifications. We present a solution with Frequentist-Bayes (FreB), a mathematically rigorous protocol that reshapes AI-generated posterior probability distributions into (locally valid) confidence regions that consistently include true parameters with the expected probability, while achieving minimum size when training and target data align. We demonstrate FreB's effectiveness by tackling diverse case studies in the physical sciences: identifying unknown sources under dataset shift, reconciling competing theoretical models, and mitigating selection bias and systematics in observational studies. By providing validity guarantees with interpretable diagnostics, FreB enables trustworthy scientific inference across fields where direct likelihood evaluation remains impossible or prohibitively expensive.